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<a NAME="E1:52_1_1"/>
<font color="Maroon" title="c4">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">O</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">q</font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E1:52"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E2:52_1_1"/><b>then </b>
<font color="Maroon" title="c4">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">O</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font>, <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> : <font color="Maroon" title="c3">d</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b3">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b4">b</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="lattice5.html#D14" target="_self" title="LATTICE5:def.14">Def14</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c7">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c9">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font><b> such that </b><br/><a NAME="E4:52_1_1"/><i><font color="Green" title="E38">A2</font></i>: 
( <font color="Maroon" title="c4">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> &amp; <font color="Maroon" title="c3">d</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c9">b</font> )
 ;<br/>
<a NAME="E5:52_1_1"/><i><font color="Green" title="E39">A3</font></i>: 
( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> &amp; <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> )
 
;<br/>
<a NAME="E6:52_1_1"/>
<font color="Maroon" title="c1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c5">O</font>
 
<b>by </b><i><a class="ref" href="lattice5.html#T27" target="_self" title="LATTICE5:th.27">Th27</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c10">x</font> = <font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c11">y</font> = <font color="Maroon" title="c7">y</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c5">O</font> <b>by </b><i><a class="txt" href="lattice5.html#E5:52_1_1"><i><font color="Green" title="E39">A3</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">a</font> = <font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c13">b</font> = <font color="Maroon" title="c9">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c14">z</font> = <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font>,<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">b</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c5">O</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c5">O</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span> ;<br/>
<a NAME="E10:52_1_1"/>
<font color="Maroon" title="c14">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">O</font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E4:52_1_1"><i><font color="Green" title="E38">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E11:52_1_1"/>
<font color="Maroon" title="c4">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">O</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c5">O</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c5">O</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span>
 ;<br/>


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